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library(dplyr)

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

    filter, lag

The following objects are masked from ‘package:base’:

    intersect, setdiff, setequal, union

library(ggplot2)
library(tidyr)

Attaching package: ‘tidyr’

The following object is masked _by_ ‘.GlobalEnv’:

    billboard

library(car)

Warning: package ‘car’ was built under R version 4.3.2Loading required package: carData
Warning: package ‘carData’ was built under R version 4.3.2
Attaching package: ‘car’

The following object is masked from ‘package:dplyr’:

    recode

library(MASS)

Attaching package: ‘MASS’

The following object is masked from ‘package:dplyr’:

    select

The following object is masked from ‘package:plotly’:

    select

library(repr)

Warning: package ‘repr’ was built under R version 4.3.2

library(pals)

Warning: package ‘pals’ was built under R version 4.3.2

library(ggpubr)

Warning: package ‘ggpubr’ was built under R version 4.3.2

library(plotly)

ecars_raw = read.csv('EV_cars.csv')
ecars_raw = ecars_raw %>% rename(Price = Price.DE., Acceleration = acceleration..0.100.)
make = strsplit(ecars_raw$Car_name, split = ' ')

make_ = c()
n = length(make)

for (i in 1:n) {
  make_[i] = make[[i]][1]
}

ecars_raw$Make = make_

ecars_raw = ecars_raw %>% relocate(Make, .before = Car_name_link)
ecars_raw = ecars_raw %>% relocate(Battery, .after = Car_name_link)

ecars_raw = ecars_raw %>% filter(!is.na(Fast_charge))
ecars = ecars_raw %>% filter(!is.na(Price))
ecars_missing_price = ecars_raw %>% filter(is.na(Price))

ecars

ecars_missing_price

plot(ecars[,4:10], 
     main = 'Comparison of all Quantitive Features') 

top_10 = ecars %>% group_by(Make) %>%
  filter(n() >= 10)

top_10

make_colors = c('#e6194b', '#f58231',  '#ffe119', 
                '#bcf60c','#3cb44b', '#008080',
                '#aaffc3', '#4363d8', '#000075',
                '#46f0f0', '#911eb4', '#e6beff',
                '#f032e6', '#fabebe')

make_colors2 = c('#e6194b', '#f58231',  '#ffe119', 
                '#bcf60c','#3cb44b', '#008080',
                '#aaffc3', '#4363d8', '#000075',
                '#46f0f0', '#911eb4', '#e6beff',
                '#f032e6', '#fabebe', 'black')

make_other = unique(ecars$Make2)
make_other = sort(make_other)
make_other[15] = 'Other'
make_other

 [1] "Audi"       "BMW"        "Citroen"    "Fiat"      
 [5] "Hyundai"    "Mercedes"   "MG"         "NIO"       
 [9] "Opel"       "Peugeot"    "Porsche"    "Tesla"     
[13] "Volkswagen" "Volvo"      "Other"     

ggplot(ecars, aes(x = Battery, y = Price, text = Car_name)) +
  geom_point(aes(col = Make2)) + 
  scale_color_manual(name = "Make", values = make_colors2, labels = make_other)+
  xlab("Battery Capacity (kWh)") + 
  ylab("Price in Germany (euros) ") +
  ggtitle('Electric Vehicle Battery vs. Price (Makes with 10+ Models Highlighted)') +
  theme(legend.position = "bottom")

Range_Bat = lm(Range ~ Battery, data = ecars)
summary(Range_Bat)

Call:
lm(formula = Range ~ Battery, data = ecars)

Residuals:
     Min       1Q   Median       3Q      Max 
-152.015  -27.740    6.636   34.682  123.700 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  39.1986    10.8427   3.615 0.000351 ***
Battery       4.6424     0.1461  31.780  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 52.04 on 305 degrees of freedom
Multiple R-squared:  0.7681,    Adjusted R-squared:  0.7673 
F-statistic:  1010 on 1 and 305 DF,  p-value: < 2.2e-16

plot(Range_Bat)

price_model_empty = lm(Price ~ 1, data = ecars)
price_model_full= lm(Price ~ Battery + Efficiency + Fast_charge + Range + Top_speed + Acceleration, data = ecars)
summary(price_model_full)

Call:
lm(formula = Price ~ Battery + Efficiency + Fast_charge + Range + 
    Top_speed + Acceleration, data = ecars)

Residuals:
   Min     1Q Median     3Q    Max 
-53557 -11739   -178   8223  84430 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -1.613e+05  2.398e+04  -6.724 8.91e-11 ***
Battery       2.215e+02  3.506e+02   0.632  0.52798    
Efficiency    3.052e+02  1.140e+02   2.678  0.00781 ** 
Fast_charge   1.785e+01  7.819e+00   2.283  0.02315 *  
Range         9.066e+00  6.679e+01   0.136  0.89211    
Top_speed     7.013e+02  7.086e+01   9.897  < 2e-16 ***
Acceleration  1.762e+03  7.746e+02   2.274  0.02366 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 18530 on 300 degrees of freedom
Multiple R-squared:  0.7167,    Adjusted R-squared:  0.711 
F-statistic: 126.5 on 6 and 300 DF,  p-value: < 2.2e-16

scope = list(lower = formula(price_model_empty), upper = formula(price_model_full))
forwardAIC = step(price_model_empty, scope, direction = 'forward', k = 2)

Start:  AIC=6415.84
Price ~ 1

               Df  Sum of Sq        RSS    AIC
+ Top_speed     1 2.1023e+11 1.5319e+11 6152.6
+ Battery       1 1.7911e+11 1.8431e+11 6209.4
+ Fast_charge   1 1.3923e+11 2.2419e+11 6269.5
+ Range         1 1.2615e+11 2.3728e+11 6287.0
+ Acceleration  1 1.0296e+11 2.6046e+11 6315.6
+ Efficiency    1 1.1067e+10 3.5235e+11 6408.3
<none>                       3.6342e+11 6415.8

Step:  AIC=6152.62
Price ~ Top_speed

               Df  Sum of Sq        RSS    AIC
+ Efficiency    1 4.2802e+10 1.1039e+11 6054.0
+ Battery       1 1.9965e+10 1.3322e+11 6111.8
+ Acceleration  1 1.5065e+10 1.3812e+11 6122.8
<none>                       1.5319e+11 6152.6
+ Fast_charge   1 2.2387e+08 1.5297e+11 6154.2
+ Range         1 7.0491e+07 1.5312e+11 6154.5

Step:  AIC=6054.03
Price ~ Top_speed + Efficiency

               Df  Sum of Sq        RSS    AIC
+ Fast_charge   1 3519695484 1.0687e+11 6046.1
+ Range         1 3506122724 1.0688e+11 6046.1
+ Battery       1 3063673448 1.0732e+11 6047.4
+ Acceleration  1  915987463 1.0947e+11 6053.5
<none>                       1.1039e+11 6054.0

Step:  AIC=6046.08
Price ~ Top_speed + Efficiency + Fast_charge

               Df  Sum of Sq        RSS    AIC
+ Range         1 2137906570 1.0473e+11 6041.9
+ Battery       1 2032210165 1.0484e+11 6042.2
+ Acceleration  1  713779942 1.0615e+11 6046.0
<none>                       1.0687e+11 6046.1

Step:  AIC=6041.87
Price ~ Top_speed + Efficiency + Fast_charge + Range

               Df  Sum of Sq        RSS    AIC
+ Acceleration  1 1639080066 1.0309e+11 6039.0
<none>                       1.0473e+11 6041.9
+ Battery       1    1076868 1.0473e+11 6043.9

Step:  AIC=6039.03
Price ~ Top_speed + Efficiency + Fast_charge + Range + Acceleration

          Df Sum of Sq        RSS    AIC
<none>                 1.0309e+11 6039.0
+ Battery  1  1.37e+08 1.0295e+11 6040.6

price_model_initial = lm(Price ~ Efficiency + Fast_charge + Range + Top_speed + Acceleration, data = ecars)

summary(price_model_initial)

Call:
lm(formula = Price ~ Efficiency + Fast_charge + Range + Top_speed + 
    Acceleration, data = ecars)

Residuals:
   Min     1Q Median     3Q    Max 
-53655 -11767   -328   8350  82937 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -1.731e+05  1.497e+04 -11.561  < 2e-16 ***
Efficiency    3.730e+02  3.831e+01   9.736  < 2e-16 ***
Fast_charge   1.699e+01  7.692e+00   2.208  0.02797 *  
Range         4.992e+01  1.669e+01   2.991  0.00301 ** 
Top_speed     7.047e+02  7.058e+01   9.984  < 2e-16 ***
Acceleration  1.637e+03  7.485e+02   2.188  0.02947 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 18510 on 301 degrees of freedom
Multiple R-squared:  0.7163,    Adjusted R-squared:  0.7116 
F-statistic:   152 on 5 and 301 DF,  p-value: < 2.2e-16

plot(price_model_initial)

bc = boxCox(price_model_initial)

lambda = bc$x[which(bc$y == max(bc$y))]

ecars$Price_lambda = (ecars$Price^lambda - 1)/lambda

price_model = lm(Price_lambda ~ Efficiency + Fast_charge + Range + Top_speed + Acceleration, data = ecars)

summary(price_model)

Call:
lm(formula = Price_lambda ~ Efficiency + Fast_charge + Range + 
    Top_speed + Acceleration, data = ecars)

Residuals:
       Min         1Q     Median         3Q        Max 
-2.951e-04 -4.127e-05  8.710e-06  4.794e-05  1.467e-04 

Coefficients:
               Estimate Std. Error   t value Pr(>|t|)    
(Intercept)   1.413e+00  5.206e-05 27130.409  < 2e-16 ***
Efficiency    3.059e-06  1.332e-07    22.957  < 2e-16 ***
Fast_charge   1.407e-07  2.675e-08     5.259 2.75e-07 ***
Range         5.510e-07  5.805e-08     9.491  < 2e-16 ***
Top_speed     1.601e-06  2.455e-07     6.524 2.89e-10 ***
Acceleration -4.715e-06  2.603e-06    -1.812    0.071 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.436e-05 on 301 degrees of freedom
Multiple R-squared:  0.853, Adjusted R-squared:  0.8505 
F-statistic: 349.3 on 5 and 301 DF,  p-value: < 2.2e-16

plot(price_model)

broom::glance(price_model)

prediction = predict(price_model, ecars, interval = 'prediction')
confidence = predict(price_model, ecars, interval = 'confidence')
prediction_dollars = ((prediction * lambda) + 1)^(1/lambda)
confidence_dollars = ((confidence * lambda) + 1)^(1/lambda)
predicted_price = data.frame(Name = ecars$Car_name,
                             Make = ecars$Make,
                             Price = ecars$Price/1000,
                             Predicted = (prediction_dollars[,1]/1000),
                             Predict_lwr = (prediction_dollars[,2]/1000),
                             Predict_upr = (prediction_dollars[,3]/1000),
                             Confidence_lwr = (confidence_dollars[,2]/1000),
                             Confidence_upr = (confidence_dollars[,3]/1000))
predicted_price

most_makes = predicted_price %>%
  group_by(Make)%>%
  filter(n() >= 10) %>%
  summarise(mean_price = mean(Price), mean_predicted = mean(Predicted))
most_makes

prediction_missing = predict(price_model, ecars_missing_price, interval = 'prediction')
prediction_missing_dollars = ((prediction_missing * lambda) + 1)^(1/lambda)

predicted_missing_price = data.frame(Name = ecars_missing_price$Car_name,
                             Make = ecars_missing_price$Make,
                             Predicted = (prediction_missing_dollars[,1]/1000))
                           
predicted_missing_price

All EV models with average of Makes with 10+

 1 + 1

[1] 2

a = ggplot(NULL, aes(Predicted_price, Price)) +
      geom_smooth(data = predicted_price, aes(x = Predicted, y = Predicted), 
                  col = 'blue', alpha = .8) +
      geom_smooth(data = predicted_price, aes(x = Predicted, y = Predict_lwr), 
                  col = 'red', linetype = 'dashed', alpha = .8) +
      geom_smooth(data = predicted_price, aes(x = Predicted, y = Predict_upr), 
                  col = 'red', linetype = 'dashed', alpha = .8) +
      geom_smooth(data = predicted_price, aes(x = Predicted, y = Confidence_lwr), 
                  col = 'black', linetype = 'dashed', alpha = .8) +
      geom_smooth(data = predicted_price, aes(x = Predicted, y = Confidence_upr), 
                  col = 'black', linetype = 'dashed', alpha = .8) 

a + geom_point(data = predicted_price, aes(x = Predicted, y = Price, text = Price)) +
      ylim(25, 250) + xlim(25, 250) +
      xlab("Predicted price (euros in thousands)") + ylab("Price (euros in thousands)") +
      ggtitle('Predicted Price vs. Price for all EV Models')

Warning: Ignoring unknown aesthetics: text

NA

b = a +  
    geom_point(data = predicted_price, aes(x = Predicted, y = Price, col = Make2)) +
    theme(legend.position = "bottom", legend.text = element_text(size = 8))+
    xlab("Predicted price (euros in thousands)") + ylab("Price (euros in thousands)") +
    ggtitle('Predicted Price vs. Price for all EV Models') +
    scale_color_manual(name = "Make", values = make_colors2, labels = make_other)

b +  ylim(25, 200) + xlim(25, 180) 

b +  ylim(25, 75) + xlim(25, 75) 

c = a + 
    geom_point(data = predicted_price, aes(x = Predicted, y = Price), alpha = .5) +
    geom_point(data = most_makes, aes(x = mean_predicted, y = mean_price), size = 3) +
    geom_point(data = most_makes, aes(x = mean_predicted, y = mean_price, col = Make), size = 2) +
    theme(legend.position = "bottom", legend.text = element_text(size = 8))+
    xlab("Predicted price (euros in thousands)") + ylab("Price (euros in thousands)") +
    ggtitle('Predicted Price vs. Price for all EV Models') +
    scale_color_manual(values = make_colors)

c + ylim(25, 250) + xlim(25, 250)

c + ylim(25, 75) + xlim(25, 75)

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